How do you solve this system for m and b: 342=23m+b, 147=10m +b?

1 Answer
Alan P.
Oct 31, 2016

(m,b)=(15,-3)

Explanation:

Given
[1]color(white)("XXX")342=23m+b
[2]color(white)("XXX")147=10m+b

Subtracting [2] from [1]
[3]color(white)("XXX")195=13m

Dividing both sides by 13
[4]color(white)("XXX")15=mcolor(white)("XXX")or equivalently: m=15

Substituting 15 for m in one of the given equations (I will use [2])
[5]color(white)("XXX")147=10 * (15)+b = 150 +b

Subtracting 150 from both sides
[6]color(white)("XXX")-3=bcolor(white)("XXX") or equivalently: b=-3

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